Maybe this is not a new idea, but i just came to think of a nice way to have paper notes in the Bitcoin system.
I bitcoin note would be like a paper wallet (with a private and a public key) but with the keys hidden.
As long as the note is circulated the keys remain under some safe protection (under a lightproof film or something).
Then when someone wants to "cash in" on the note then he or she removes the film, makes a payment to the own account. The notes is then of course rendered useless.
How do you know that the issuer of the paper note didn't record the private key when they created the paper note?
How do you know that someone didn't find a way to access the private key from under the film without disturbing the film (or found a way to replace the film afterwards)?